Solve the Problem $\left( { } ^ { \circ } \mathrm { F } \right)$

Multiple Choice

Solve the problem.
-Suppose that the average monthly low temperatures for a small town are shown in the table.
\begin{tabular} { l | l l l l l l l l l l l l }
Month & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\
\hline Temperature $\left( { } ^ { \circ } \mathrm { F } \right)$ & 19 & 27 & 38 & 45 & 57 & 62 & 65 & 58 & 51 & 41 & 33 & 25
\end{tabular}
Model this data using $f ( x ) = a \sin ( b ( x - c ) ) + d$ .

A) $f ( x ) = 23 \sin \left( \frac { \pi } { 6 } ( x - 7 ) \right) + 42$
B) $f ( x ) = 23 \sin \left( \frac { \pi } { 12 } ( x - 4 ) \right) + 42$
C) $f ( x ) = 23 \sin \left( \frac { \pi } { 6 } ( x - 4 ) \right) + 42$
D) $f ( x ) = 42 \sin \left( \frac { \pi } { 6 } ( x - 4 ) \right) + 23$